The meta-material is an artificial structure that behaves unlike materials in the natural world with respect to electromagnetic waves including light, and is sometimes referred to as a material having a negative refractive index.
Conventionally, a microwave resonator configured to include a composite right/left-handed meta-material using the meta-material has been proposed. In this case, the “right-handed system” indicates a propagation state of electromagnetic waves having such a directional relation that the electric field vector, the magnetic field vector, and the wave number vector of electromagnetic waves constitute a right-handed system, and indicates such a propagation state of forward waves that the direction of the transmission power of electromagnetic waves (direction of group velocity) and the direction of the phase plane (direction of phase velocity) are directed to the same direction. This state is possible in a medium and a structure body of which the effective permittivity and permeability both have positive values. In addition, the “left-handed system” indicates a propagation state of electromagnetic waves having such a directional relation that the electric field vector, the magnetic field vector, and the wave number vector of electromagnetic waves constitute a left-handed system, and indicates such a propagation state of backward waves that the direction of the transmission power of electromagnetic waves and the direction of the phase plane are directed to opposite directions to each other. This state is possible in a medium and a structure body of which the effective permittivity and permeability both have negative values.
There are proposed several methods for constituting meta-materials, and the two of a resonant type meta-material and a transmission line (non-resonant) type meta-material can be enumerated as representative examples. The former resonant type meta-material is configured to include a combination of magnetic and electric resonators that respond to the magnetic field and electric field components of external electromagnetic fields as represented by a combination of a split ring resonator and thin lines configured to include metal strips. In this structure, the effective permittivity or permeability exhibits an anti-resonance characteristic, and therefore, a loss exerts a very large influence in the vicinity of the resonance frequency. On the other hand, in the latter transmission line type meta-material, the structure body is configured by using the fact that the general propagation style of electromagnetic waves can be described by a transmission line model. The conventional one-dimensional right-handed meta-material structure that permits forward wave propagation has such a ladder type structure that an inductive element is inserted in its series branch and a capacitive element is inserted in its parallel branch (hereinafter also referred to as a shunt branch), in contrast to which the one-dimensional left-handed meta-material structure has such a structure that its capacitive element is inserted in the series branch and its inductive element is inserted in the parallel branch in order to make the effective permittivity and permeability values negative. Many of the transmission line type meta-materials, which do not exhibit the anti-resonance characteristics in the effective permittivity and permeability, therefore has such a feature that it has a loss lower than that of the aforementioned resonant type. Since the transmission line type meta-material operates as a right-handed meta-material, and a left-handed meta-material, a single negative meta-material in which either one of permittivity or permeability becomes negative and the other becomes positive, or a meta-material in which the effective permittivity or permeability is zero depending on the operating frequency band, it is called a composite right/left-handed meta-material.
In general, the effective permittivity and permeability of the composite right/left-handed meta-material assume a value of zero at different frequencies. In the above case, in a band between adjacent frequency at which the permittivity is zero and the frequency at which the permeability is zero, either one of permittivity and permeability assumes a negative value, and the other assumes a positive value. In this case, the propagation conditions of electromagnetic waves are not satisfied, and a forbidden band is formed. The meta-material operates as a left-handed meta-material since permittivity and permeability are both negative in a band on the lower side of this forbidden band or operates as a right-handed meta-material since they have positive values in a band on the upper side. When the frequencies at which the permittivity and permeability become zero coincide with each other, no forbidden band (band-gap) is formed, and the left-handed transmission band and the right-handed transmission band are continuously connected together. Such a meta-material is called the balanced composite right/left-handed meta-material, and the opposite type is called the unbalanced composite right/left-handed meta-material. In the balanced composite right/left-handed meta-material, not only the forbidden band is not generated but also the group velocity does not become zero even at a frequency at which the phase constant is zero, providing such a feature that transfer of power can be efficiently performed.
A first report concerning a zeroth-order resonator was provided in the Patent Documents 1 and 2 and the Non-Patent Document 1. This is configured by providing open or short-circuited ends at both the terminals of a composite right/left-handed transmission line of a finite length configured to include a plurality of unit cells. The resonator has such enumerable features that:                (i) the resonator resonates at a resonance frequency determined only by the structural parameters of the unit cells regardless of the line length; and        (ii) the amplitude and the phase of the electromagnetic field distribution in the resonator become uniform at the time of resonance.        
The resonance frequency of the zeroth-order resonator corresponds to a frequency at which the phase constant is zero (effective permittivity is zero or effective permeability is zero) in a dispersion diagram (relation between operating frequency and propagation constant (hereinafter, also referred to as a phase constant)) that provides the propagation characteristics of the composite right/left-handed transmission line.
Such a resonance condition that the resonance frequency is not related to the line length can be obtained in either case where both the terminals of the composite right/left-handed transmission line are open terminals or short-circuited terminals. When both the terminals are open terminals, resonance occurs at a frequency corresponding to zero effective permittivity of the line that constitutes the zeroth-order resonator. When both the terminals are short-circuited, resonance occurs at a frequency corresponding to zero effective permeability. Therefore, it has been the designing method of the conventional resonator that the operating frequency of the zeroth-order resonator is varied depending on when both the terminals are made to be open or short-circuited in the case where the unbalanced composite right/left-handed transmission line is used.
Since the amplitude and the phase become uniform in the electromagnetic field distribution inside the zeroth-order resonator, it is possible to constitute an antenna of a sharp directivity and a high gain by applying a composite right/left-handed transmission line configured to include a large number of unit cells to an antenna. In addition, several reports of applications of zeroth-order resonators to antenna elements have already been provided (See, for example, the Non-Patent Documents 2 and 3).
However, in the zeroth-order resonator configured by employing an unbalanced composite right/left-handed transmission line whose frequency at which the effective permittivity is zero and frequency at which the effective permeability is zero are varied, the group velocity also disadvantageously becomes zero by its nature at the frequency at which the phase constant is zero on the dispersion curve that represents the propagation characteristics of the line. Accordingly, there has been such a problem that, when the number of unit cells that constitute the resonator is increased (resonator is increased in size), no resonance operation can be obtained because the signal cannot be propagated along the resonator. In practice, many of the zeroth-order resonators with use of the unbalanced composite right/left-handed transmission line proposed up to now are configured to include a comparatively smaller number of unit cells, and they are not suitable for an increase in the size of the antenna. For the above reasons, it is required to constitute a line of which the group velocity is not zero even when the phase constant is zero, and it is required to employ a balanced composite right/left-handed transmission line.
There has already been such a report that attempts to design a directional antenna and improve the gain by employing the resonator as an antenna element with the zeroth-order resonator size increased (See, for example, the Non-Patent Documents 4, 5 and 6). According to the reports of the Non-Patent Documents 4 and 5, a one-dimensional zeroth-order resonator configured to include such a composite right/left-handed transmission line that capacitors are periodically inserted in the series branch of the micro-strip line and short-circuit stubs are periodically inserted as inductive elements in the parallel branch is adopted in each case. In addition, regarding improvements in the directivity and the radiation gain of the antenna having a large number of unit cells, only numerical calculation results have been reported. On the other hand, the Non-Patent Document 6 describes an application of a two-dimensional zeroth-order resonator configured to include a composite right/left-handed meta-material structure configured to include a combination of a dielectric resonator and parallel plate lines as a directional antenna element.
Further, a filter, a power distributor, an oscillator and so on can be enumerated as applications other than the antenna, and several report examples are provided (See, for example, the Non-Patent Document 7).